Courses

Representation Theory of the Symmetric Group, its Hecke Algebra, and their Generalisations. Maria Chlouveraki (National and Kapodistrian University of Athens).

Abstract: The representation theory of the symmetric group is a cornerstone of modern algebra, celebrated for its profound connections to combinatorics. This 5-hour course provides a journey from the classical theory to its rich modern generalisations. We will begin by exploring the symmetric group, establishing the foundational combinatorial tools—partitions, Young diagrams, and standard tableaux—that construct and classify its irreducible representations.

Building on this, we will introduce the Iwahori-Hecke algebra of Type A, viewing it as a deformation of the symmetric group algebra, and observe how the classical combinatorial machinery naturally adapts to this deformed setting. We will then extend this framework to the complex reflection groups G(d,1,n) and their associated deformations, the Ariki-Koike algebras. Throughout the lectures, a strong emphasis will be placed on the combinatorial structures, particularly the transition from simple partitions to multipartitions. Time permitting, the course will conclude with a brief look at further extensions, such as Yokonuma-Hecke algebras, or an exploration of how these algebraic structures are applied in knot theory.

Combinatorial polytope theory. Vincent Pilaud (Universitat de Barcelona).

Abstract: a detailed abstract will be added soon.

SageMath: research and experimentation in Combinatorics. Viviane Pons (Paris-Saclay University).

Abstract: The course presents the mathematical software SageMath and, more specifically, its usage for research in combinatorics. We will focus on families of combinatorial objects, especially related to the Tamari lattice, and their implementation in the context of object oriented programming.